Generation and spectroscopic characterization of continuous-wave 148.4-nm light in strontium tetraborate

Introduction

The $^{229}\mathrm{Th}$ nucleus has a low-lying isomeric state at 8.4 eV, that is, at 148.4 nm, and it is currently the only nuclear transition within reach of table-top laser technology [1]. Its energy is largely decoupled from the electronic shell, so the transition should be exceptionally narrow, and the isomer could serve as a solid-state clock, embedded in a vacuum-ultraviolet (VUV) transparent crystal [2], or as an ion clock that inherits the stability of an optical atomic clock [3] while being far less sensitive to external perturbations [4]. The isomer has been detected through its internal conversion decay [5], its excitation energy measured to sub-eV precision [6], and the transition pumped by X-rays [7]. Its radiative decay has been observed [8], the transition driven by a laser [9] and characterized spectroscopically [10, 11, 12], and its frequency ratio to a $^{87}\mathrm{Sr}$ clock measured with a VUV frequency comb [13]. After the laser Mössbauer spectroscopy in a solid-state host [14], nuclear clock operation with 148-nm light from four-wave mixing [15, 16] or from solid-state VUV sources [17, 18, 19, 20] has also been reported. All of these experiments need narrow-line continuous-wave (CW) radiation at 148.4 nm whose power, spectral purity and stability can be measured and controlled [21].

The most direct route to such radiation is second-harmonic generation (SHG) of 296.8-nm light. Strontium tetraborate (SrB$_4$O$_7$, SBO) cannot be birefringently phase-matched in this range, but the random orientation of its antiparallel ferroelectric domains provides random quasi-phase matching (RQPM) [22, 23], which has already delivered coherent VUV radiation down to 121 nm [24]. Single-pass CW conversion in SBO reaches 1.3 nW at 325 mW of pump power [18], 1.7 nW at 580 mW [25] and 8.1 nW at 920 mW [20]. Quasi-phase-matched BaMgF$_4$ reaches tens of picowatts at about 1 W [26, 27], while resonant conversion in Cd vapour has delivered CW 148.4-nm radiation at the 10 μW level with a linewidth of about 100 Hz [15, 28]. For a solid-state nuclear clock, the laser source has to operate over timescales of hours. Its temperature dependence, spatial uniformity and behaviour under prolonged irradiation therefore affect the design of an experiment as directly as its output power; all three have to be characterized before such a source can be used in a clock.

Such a characterization is not simply a matter of pointing a detector at the beam. Molecular oxygen absorbs 148.4-nm light so strongly [29] that a few millimetres of air already remove most of it, so the light has to travel in nitrogen, helium or vacuum. Due to low conversion efficiency of RQPM ($\sim10^{-9}$), and the low efficiency of the VUV optical devices, the signal usually reduced to picowatt level on the detector, thus increasing the difficulty to detect the signal. Therefore, seldom spectrometers work in this wavelength domain. Reported solutions place a solar-blind CsI photomultiplier tube (PMT) behind a stack of VUV bandpass filters in an evacuated chamber [25], or use a commercial vacuum grating spectrometer [18]. Both work well, but the filters fix the passband and cannot read the exact wavelength, while a grating instrument is limited by the strict geometric configuration, increasing the difficulties to detect the signal in the vacuum system. Thus, for the RQPM conversion of SBO in the VUV region, an setup which can tell the wavelength and the power is limited.

Here we report CW $148.4$-nm generation in SBO and a complete spectroscopic characterization of the light that it delivers, obtained with a compact prism spectrometer built for the purpose. Instead of rejecting the fundamental with coatings, we disperse the light with a CaF$_2$ prism and scan the spectrum with a $100\,\mu\mathrm{m}$ slit in front of a solar-blind PMT on a rotation stage, so that the wavelength is encoded in the PMT angle; dichroic mirrors and a baffle tube suppress the scattered pump before dispersion, the path sits in a chamber that is evacuated and then filled with nitrogen, and the angle-to-wavelength relation is calibrated. The setup can capture the signal photons, and detect the picowatt VUV siganl. With this spectrometer, our measurements show that the harmonic follows the quadratic law expected for SHG, establish an absolute power, and measure how the conversion depends on the crystal position, on the temperature, and on the irradiation history. The most striking of these is the temperature response, which is not a single smooth optimum but a sequence of maxima and minima only a few degrees apart.

Method

Crystal growth and sample preparation

The SBO crystal was grown by the Czochralski method [30] at the Technical Institute of Physics and Chemistry, Chinese Academy of Sciences (Beijing). High-purity ($99.99\%$) boric acid (H$_3$BO$_3$) and strontium carbonate (SrCO$_3$) were weighed in stoichiometric ratio and mixed, and the furnace was held close to the melting point of SrB$_4$O$_7$ while the crystal was pulled along the $a$ axis at $2$ mm/day. Ten days of growth gave a transparent boule of $45 \times10 \times15$ mm$^3$. A $1$ mm thick $a$-cut plate was cut from it, with only its surfaces polished and no coating applied; X-ray diffraction confirmed the orientation before the SHG measurements.

Optical layout

The layout is shown in Figure 1. The $296.8$-nm pump (Precise Laser) is focused by Lens 1 ($f = 300$ mm) through the entrance window into the SBO crystal, which sits on a four-axis stage (translation along XYZ, rotation around X) that sets both the pump focus and the crystal region sampled by the beam. The crystal and Lens 2 ($f = 150$ mm) are enclosed in a light-baffle case that blocks scattered light originating from the pump.

Lens 2 collimates the output, and a pair of dichroic mirrors (DCM) folds the beam into the dispersive arm; each reflection reflects the VUV and transmits part of the pump out of the path, so the double bounce attenuates the residual fundamental by about six orders of magnitude before the beam reaches the prism. An $80$ mm baffle tube (the collimator in Figure 1) then accepts a cone of about $0.7^\circ$ through its $1$ mm entrance slit and keeps light scattered at larger angles away from the prism; the second slit drawn behind it in Figure 1 is fully open ($2$ mm) and does not act on the beam. The aperture that defines the instrument is the $100\,\mu\mathrm{m}$ slit directly in front of the PMT, which selects a small angular and spatial fraction of the dispersed beam and therefore sets the sampling of the spectrum.

The collimated beam enters a CaF$_2$ prism (PS863, Thorlabs) of apex angle $A = 60^\circ$. Refraction at the two faces obeys

where $n(\lambda)$ is the refractive index and $\delta$ the deflection angle. Because $n$ rises steeply towards short wavelengths in the VUV, the $148.4$-nm beam is deviated more strongly than the $296.8$-nm pump. A solar-blind CsI PMT (R10454, Hamamatsu) is carried by a rotation stage (Lab65.RS, Multi-Field) mounted below the prism, with its axis through the refracting corner; a rigid arm links the PMT to the stage and points at the axis, so rotating the stage carries the PMT around the prism at a fixed distance. The prism-to-PMT distance is about $150$ mm, so one degree of $\theta_{\mathrm{PMT}}$ corresponds to $2.6$ mm of travel. The PMT records the light as a function of the angle $\theta_{\mathrm{PMT}}$ measured from the X direction (Figure 1), so that $\delta= 90^\circ-\theta_{\mathrm{PMT}}$.

The whole optical path is enclosed in a sealed chamber (Figure 1). Before each run the chamber is pumped to about $1 \times10^{-3}$ Pa and then back-filled with dry nitrogen through the inlet, so the spectrometer can be run either in vacuum or in a nitrogen atmosphere.

Dispersion and wavelength calibration

For a prism operated at minimum deviation, Eq. (1) gives the angular dispersion as

so the separation of two lines grows with the material dispersion $\mathrm{d}n/\mathrm{d}\lambda$ and with the apex angle. CaF$_2$ is used because it combines transparency down to about 120 nm with a dispersion that is large in the VUV: Eq. (2) gives about 1.7 nm/$^\circ$ at 148.4 nm and 30 nm/$^\circ$ at 296.8 nm.

The wavelength scale is calibrated with a deuterium lamp (L2D2, Hamamatsu) and a reference VUV spectrometer (VS7550, Resonance Ltd.). The lamp is placed at the position of DCM2 and its output is directed to the collimator, while the reference spectrometer with a 100 $\mu$m input aperture is mounted on the rotation-stage arm; the inset of Figure 2 shows the 148.22 nm feature, fitted with a Gaussian ($\mu= 148.22$ nm, $\sigma= 1.34$ nm), recorded with the reference spectrometer turned to the appropriate angle to the prism. Figure 2 compares the deflection angles measured in this way between 130 and 185 nm (blue points) with the angles calculated from Eq. (1) using the Sellmeier data of CaF$_2$ (green points) [31, 32]; between 140 and 180 nm the two agree to within about 1.5°. The calculation extends to 300 nm and thus covers the 296.8-nm pump. To map $\theta_{\mathrm{PMT}}$ to wavelength, each measured line centre is then fitted as a function of $\theta_{\mathrm{PMT}}$ with a fourth-order polynomial,

with $a_0 = 3.651 \times10^3$, $a_1 = -3.627 \times10^2$, $a_2 = 1.399 \times10^1$, $a_3 = -2.40 \times10^{-1}$, and $a_4 = 1.552 \times10^{-3}$, where $\theta_{\mathrm{PMT}}$ is in degrees and $\lambda$ in nanometres; applied to the recorded spectra, the fit produces the wavelength scale shown on their upper axes (Figure 3).

As a check at the two wavelengths of interest, the SHG beam itself provides an internal reference: the 148.4-nm line measured below sits at $\theta_{\mathrm{PMT}} = 43.8^\circ$, which Eq. (3) maps to 148.7 nm, and the 296.8-nm pump sits at $\theta_{\mathrm{PMT}} = 55.0^\circ$, which the same calibration maps to 295 nm; both agree with the nominal wavelengths to within the width of the lines.

Detection efficiency and data acquisition

Background is controlled at three stages: the light baffle blocks scattering at the crystal, the dichroic pair removes most of the fundamental before dispersion, and the angular selection of the PMT rejects light that is not deviated onto the detector. The residual is measured with the PMT parked between the two lines; with the pump on a bright RQPM spot, the 148.4-nm line reaches $1.4 \times10^4$ cps against $1.0 \times10^3$ cps between the lines (Figure 3).

The count rate is converted into a VUV power through the overall efficiency of the detection channel,

where $\epsilon_{\mathrm{SBO}} \approx0.2$ is the transmission of the 148.4 nm light through the 1 mm crystal, $\epsilon_{\mathrm{Lens2}} = 0.8$ and $\epsilon_{\mathrm{prism}} = 0.8$ are the transmissions of the collimating lens and of the two prism faces, $\epsilon_{\mathrm{DCM1}} = \epsilon_{\mathrm{DCM2}} = 0.6$ are the reflectivities of the two dichroics at 148.4 nm, and $Q_{\mathrm{PMT}} \approx0.2$ is the quantum efficiency of the CsI photocathode at this wavelength [33]. The product is $\epsilon_{\mathrm{det}} \approx0.9\%$.

The 100 $\mu$m slit in front of the PMT does not enter Eq. (4). Because the detector is scanned across the line, the rate integrated over the SHG profile counts every photon delivered to the slit, the slit only lowers the rate recorded at any single angle.

The absolute SHG power then follows from the total number of photoelectrons recorded across the line,

where $N$ is the integrated count rate, $E_\gamma= 8.4$ eV $= 1.34 \times10^{-18}$ J is the photon energy at 148.4 nm, and $\epsilon_{\mathrm{det}}$ is the detection efficiency of Eq. (4).

The readout is a single-photon counting chain. The PMT output is amplified ($\times25$, SR445A, Stanford Research Systems) and digitized (PXIe-5160, National Instruments); the waveforms are stored in binary, converted to ROOT files with the CERN ROOT analysis package, and histogrammed to give the count rate as a function of angle, that is, the spectrum.

Results

Spectral response and rejection of the pump

The complete spectral response of the instrument to the beam is shown in Figure 3. The pump line appears at $\theta_{\mathrm{PMT}} \approx55.0^\circ$ and the harmonic at $\theta_{\mathrm{PMT}} \approx43.8^\circ$, so that the two are separated by 11.2°. The pump is also about two orders of magnitude brighter, 1.5 $\times10^6$ cps against 1.4 $\times10^4$ cps, with a background of 1.0 $\times10^3$ cps between the lines; at the angle of the harmonic the pump therefore contributes at most 7% of the recorded rate.

Both lines have a Gaussian profile. The inset of Figure 4 gives $\sigma= 0.152^\circ$ for the harmonic, an angular FWHM of 0.36°, while the pump line is about twice as wide at 0.7°. Divided by the local dispersion of the calibration (upper axis of Figure 3), these widths correspond to $\delta\lambda\approx0.6$ nm at the harmonic and 20 nm at the pump. The first of the two is an upper bound rather than a measure of the resolution: the 100 µm slit subtends only $0.038^\circ$ at the prism, an order of magnitude less than the recorded width, so the profile is that of the beam size ($\phi\approx1$ mm) and not of the linewidth. For the purpose of this work the margin is what matters, and the separation of the two lines, $11.2^\circ$, exceeds either width by an order of magnitude.

The same figure contrasts a scan in vacuum (blue line) with one recorded with the chamber open to air (green line). In air the 148.4-nm line disappears while the pump is unchanged, as expected from the absorption length of molecular oxygen at this wavelength [29], which is a few tens of micrometres at atmospheric pressure; the whole beam path, from the crystal to the PMT, therefore has to be purged or evacuated. In vacuum, however, the SHG peak is in turn not stable: a first scan across the line shows the peak, a second records less than half of it, and in a third the peak is barely distinguishable from the background, although each scan took only a few minutes. The rapid loss points to a radiation-induced change at the irradiated spot, and prolonged irradiation in vacuum colours the whole crystal [Fig. 5(c)]. Nitrogen is transparent at 148.4 nm and also helps to carry heat away from the irradiated region, which protects the crystal. We therefore acquired all spectra reported below with the chamber filled with dry nitrogen.

Quadratic scaling and line shape

Figure 4 identifies the detected light as the second harmonic. Its inset zooms in on $\theta_{\mathrm{PMT}}$ around the 148.4-nm line and fits the peak with a Gaussian on a constant background; the amplitude is labelled “SHG” and the constant “Base”, standing for the 148.4-nm signal and for the background of scattered pump light. Over the whole range explored, 100–1100 mW, the SHG count rate (blue points) grows quadratically with the pump power,

as a second-order process should: a fit with $s = aP^2$ gives $a = (695.2 \pm9.9) \times10^{-9}$ Mcps mW$^{-2}$, where $s$ is the height of the SHG line in megacounts per second (Mcps) and $P$ the 296.8-nm pump power in milliwatts (mW). The background “Base” (green points) grows linearly with the pump power, so the signal-to-background ratio improves steadily as the pump is raised.

Spatial uniformity and stability of the conversion

Since the 148.4-nm signal comes from RQPM, the conversion is far from uniform over the crystal. Figure 5(a) maps the 148.4-nm count rate with the PMT moved to the SHG maximum of the inset of Figure 4 and the sample translated in its $X$-$Z$ plane with the pump focus fixed (Figure 1). The RQPM signal is concentrated in a region around $X \approx1$ mm and $Z \approx4$–8 mm, where the recorded rate reaches the upper end of the colour scale, and it falls to the background for $X > 2$ mm and $Z < 3.5$ mm; the contrast between the two areas is an order of magnitude. Such a map is the spatial fingerprint of RQPM [22, 24]: the inhomogeneity sampled by the beam is an average over randomly oriented domains, so translating the crystal by a few millimetres samples a different realization of the same ensemble. In practice the four-axis stage is not only an alignment tool but the control that sets the VUV power, and Figure 5(a) is the scan by which a useful region is found.

Long-term operation changes the crystal itself. Figure 5(b) and Figure 5(c) show the same crystal before and after $\sim30$ h of irradiation at $\sim1$ W in vacuum. The initially colourless crystal has turned yellow-brown: colour centres absorbing in the visible have been created by the pump radiation, consistent with the defect-related absorption of SBO studied in Ref. [34]. A CW source has to sit on the same crystal region for hours, so this is the process that will eventually limit the VUV power.

Temperature dependence of the conversion

The conversion efficiency is also sensitive to the crystal temperature. Figure 6 shows the 148.4-nm count rate and the sample temperature, recorded simultaneously in nitrogen as the crystal is heated to approximately 52 °C and subsequently allowed to cool. Over this temperature excursion, the count rate varies from $2.5 \times10^{3}$ to $6.3 \times10^{3}$ cps, corresponding to a factor of 2.5. When plotted against the sensor-read temperature [Figure 6(c)], reconstructed from the two time traces, the data exhibit a hysteresis-like loop rather than a single-valued dependence, indicating that the optical response is correlated with the measured sample temperature and may also depend on the thermal history.

A second notable feature is the multi-peaked temperature dependence, which, to our knowledge, has not previously been reported for second-harmonic generation in SBO. Rather than exhibiting a single smooth maximum, the signal displays multiple peaks and valleys. In the time trace [Figure 6(a)], the count rate passes through at least three maxima before entering a slowly decaying tail. When plotted against temperature [Figure 6(c)], the same data reveal local maxima near 34 °C, 42 °C and 47 °C, separated by local minima near 37 °C, 46 °C and 51 °C. The neighbouring extrema are separated by only a few degrees, while the count-rate contrast between a maximum and an adjacent minimum approaches the overall factor of 2.5 observed during the temperature excursion. Notably, after the minimum near 51 °C the count rate turns upward again, which suggests additional structure beyond the range explored here. Further measurements over an extended temperature range will be needed to characterize these features and clarify their underlying mechanisms.

A single thermo-optic phase-matching condition cannot produce such a structure: it would give one broad maximum, displaced smoothly by the temperature. A natural reading is that the random domain structure samples a distribution of quasi-phase-matching periods, so that different groups of domains satisfy the matching condition at different temperatures; the crystal then behaves as a set of partially independent converters that are switched on and off in succession as the temperature is swept, and the recorded curve is their sum. The same picture, together with the thermal inertia of the sample, the thermal expansion of the random domain structure, a thermo-optic change of the RQPM condition and pump-induced heating, also accounts for the lag of the optical response behind the sensor reading in Figure 6(c). Whichever mechanism dominates, the consequence for a future experiment is direct: the temperature has to be held on a chosen maximum and not merely held constant.

Absolute power and overall performance

The absolute power follows from the integrated rate. The line recorded through the 100 $\mu$m slit is a Gaussian in $\theta_{\mathrm{PMT}}$ with $\sigma= 0.15^\circ$, and its integral is about twelve times the peak of the recorded histogram. At the highest pump power the peak reaches 1.1 Mcps, so 13 Mcps of 148.4-nm photons reach the PMT; with the detection efficiency of Eq. (4), Eq. (5) gives 1.9 nW at 148.4 nm generated in the crystal. Since the signal can be raised by a factor of 2.5 by tuning the crystal to its optimum temperature (Figure 6), the achievable power is about 4.8 nW.

Discussion

The prism spectrometer trades spectral range for simplicity: it disperses the whole 120–300 nm window, so one detector can follow any line in it without changing filters or refocusing, at the price of a point-by-point scan. Because the slit is an order of magnitude narrower than the image of the line, the resolution is set by the divergence of the collimated beam, and a wider slit would raise the count rate per point without loss of resolution; coating the prism faces, or chopping the pump and detecting with a lock-in amplifier, would shorten the scan and lower the background. The same arrangement applies to any VUV source that has to be characterized before it is brought onto the nucleus.

We have demonstrated a CW 148.4-nm light source delivering an output power of 1.9 nW at room temperature, increasing to 4.8 nW when the crystal is maintained at its optimum temperature. This output power places the source within the range relevant to absorption spectroscopy of the $^{229}$Th isomer in a host crystal [18, 19], and the recorded line width establishes an upper bound of $\delta\lambda\approx0.6$ nm on its spectral width.

Bringing this source to the nucleus will require holding the crystal on a chosen maximum for hours while monitoring the conversion with the beam on the sample, which the present arrangement already permits. Three properties of the conversion have to be handled in any clock design. First, the usable aperture is small: the conversion varies by an order of magnitude over the crystal and is concentrated in a region about a millimetre across, so the position of the crystal is a control parameter of the source and not a fixed property. Second, the temperature dependence is multi-peaked, with extrema a few degrees apart, so that stabilizing the source to a single set point is not enough; the point has to sit on a chosen maximum and be held there to a fraction of the peak spacing. Third, prolonged irradiation in vacuum colours the crystal and reduces the output within hours, which limits the operating life of a solid-state emitter and favours operation in nitrogen, at reduced pump power, or with periodic annealing.

Conclusion

We have generated CW 148.4-nm light in strontium tetraborate by RQPM and characterized it spectroscopically with a view to the $^{229}$Th nuclear transition. A compact prism spectrometer built in this work reaches picowatt sensitivity without filters or a grating; calibrated against a deuterium lamp, it separates the harmonic from the 296.8-nm pump by angle alone and measures an absolute power of 1.9 nW at 148.4 nm under pumping by about 1 W at 296.8 nm. The harmonic profile has an angular FWHM of 0.36°, corresponding to a convolution-limited spectral width of about 0.6 nm rather than the intrinsic linewidth; scaling the measured temperature dependence gives 4.8 nW at the best observed temperature. The SHG conversion depends quadratically on the pump power and is far from uniform: it varies by an order of magnitude over the crystal, decays under prolonged irradiation in vacuum, and, most importantly, passes through several local maxima and minima within a 20°C wide temperature window, so that the source has to be stabilized on a chosen maximum rather than merely held constant. These measurements provide valuable information on the realization and characterization of a high-quality 148.4-nm light source, and pave the way for the future development of high-performance nuclear optical clocks.

Funding. Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0920000); National Natural Science Foundation of China (12604402, 12404314, U21A20435); CAS Project for Young Scientists in Basic Research (YSBR-055); Postdoctoral Fellowship Program of CPSF (GZB20240765); China Postdoctoral Science Foundation (2024M763347, 2025HBBSHXF017); Hubei Provincial Natural Science Foundation of China (2025AFA004, 2026AFA0888).

Acknowledgment. We thank Prof. Yunquan Liu of Peking University for providing the VUV spectrometer for the wavelength calibration.

Disclosures. The authors declare no conflicts of interest.

Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.